KASHIWARA, Masaki

Masaki Kashiwara is working on algebraic analysis, and recently on quantum groups. The most beautiful result is the introduction of the "Crystal Bases". This is obtained by a physical "intuition" that the phenomena must be simple at absolute zero temperature. In fact the representations of quantum groups have a good basis when the parameter corresponding to the temperature tends to zero. With this tool, many problems in the representations can be transformed to the combinatorial problem. Much material relating to the Young diagram and Young tableaux can be understood in this framework. Crystal bases are related with the representations of various algebras. Lascoux-Leclerc-Thibon and Ariki connect crystal bases with the representations of affine Hecke algebras of type A. I, with a graduate student N. Enomoto and V. Miemietz, introduce new crystals connected with affine Hecke algebras of type B and D.